Diagram of the adjacent picture frame has outer dimensions `=24cm xx 28` and inner dimensions `16cm xx 20`. Find the area of each section of the frame, if the width of each section is same.

The outer radius and the inner radius of a circular ring are respectively 25 cm and 24 cm.Find the area of the region which falls under the ring.

Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a rectangular tank whose dimension 55 m xx 44 m . Find the time in which the level of water in the tank will rise by 21 cm.

A pen stand made of wood is in the shape of a cuboid with four concial depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand ( see Fig. 13.16).

Rachel,an engineering student,was asked to make a model shaped like a cyclinder with two cones attached at its two ends by using a thin aluminium sheet.The diameter of the model is 3 cm and its length is 12cm.If each cone has a height of 2 cm,find the volume of air contained in the model that Rachel made.(Assume the outer and inner dimensions of the model to be nearly the same).

In a cuboidal solid metallic block of dimension 15 cm xx 10 cm xx 5 cm , a cylindrical hole of diameter 7 cm is drilled out. Find the volume and surface area of the remaining block (pi=22/7) .

Each side of a square is increased in length by 2 cm. and thereby its new area exceeds its original area by 20 cm^2 . Find the side of the square.

If twice the area of a smaller square be substracted from the area of a larger square,the difference will be 14 cm^2 .However if twice the area of the larger square is added to three times the area of smaller square.The sum would be 203 cm^2 ,How long is the side of each square.

A car has two wipes which do not overlap.Each wiper has a blade of length 25 cm seeping through an angle of 115^@ .Find the total area cleaned at each sweep of the blades.

A large steel wheel is to be fitted on to a shaft of the same material. At 27 ^@C , the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: a_ steel = 1.20 xx 10^-5K^-1 .